Theorem wl-luk-imim1i

Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. Copy of imim1i with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018)

	Ref	Expression
Hypothesis	wl-luk-imim1i.1	$$⊢\phi \to \psi$$
Assertion	wl-luk-imim1i	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imim1i.1	$$⊢\phi \to \psi$$
2		ax-luk1	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)$$